By selling a coat for Rs. 630, a shopkeeper gains 5%. Find the cost price of the coat

Options

A. Rs.700
B. Rs.625
C. Rs.600
D. Rs.650

Answer

To find the cost price of the coat given that the selling price is Rs. 630 and the profit percentage is 5%, we can follow these steps:

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Profit Percentage
The profit percentage is calculated on the cost price. The formula for selling price when profit is involved is:
\[ SP = CP + Profit \]
Where:
\[ Profit = \frac{Profit\%}{100} \times CP \]

### Step 2: Express Selling Price in terms of Cost Price
Given that the profit percentage is 5%, we can express the selling price as:
\[ SP = CP + \frac{5}{100} \times CP \]
This can be simplified to:
\[ SP = CP \left(1 + \frac{5}{100}\right) = CP \left(1 + 0.05\right) = CP \times 1.05 \]

### Step 3: Substitute the Selling Price
We know the selling price (SP) is Rs. 630, so we can write:
\[ 630 = CP \times 1.05 \]

### Step 4: Solve for Cost Price (CP)
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{630}{1.05} \]

### Step 5: Calculate the Cost Price
Now, we perform the division:
\[ CP = \frac{630}{1.05} = 600 \]

### Conclusion
The cost price of the coat is Rs. 600.

---